Filters are applied with a brush. But there's no law against airbrushing. You can apply it before or after a pin wash, it's up to you.
White spirit is a European term for mineral spirits, i.e. paint thinner. It's used for oil-based paints.
Gloss or flat: pin washes can go over a flat finish, as can filters. The 'sludge' type of wash is better over a glossy finish. The flat undercoat tends to hold onto the filter/wash, while a gloss undercoat will allow you to wipe the filter/wash off.
You can learn alot by going to Youtube and doing a search for "mig filter" or "AK interactive filter." There are plenty of demo videos out there.
Chris